Input-Output Tables

The first input is
0
. Since
3
(
0
)
+
1
=
1
, the first output is
1
.

The second input is
1
. Since
3
(
1
)
+
1
=
4
, the second output is
4
.

The
5
ordered pairs in this table can be plotted and used to graph the equation, as shown.

Alternatively, you may be presented with an input-output table and asked to guess the rule for the function.

Example 2:

Guess the function rule.

x

10

16

26

100

200

y

4

7

12

49

99

With a little thought you can guess that:

y
=
1
2
x
−
1

Note that for this kind of problem, you can never say for
sure
what the function rule is, since for any finite set of ordered pairs, there are many different functions that go through them. But usually there is a fairly obvious one that you can guess.